Q18 of 113 Page 50

Find the quadratic polynomial, the sum of whose roots is √2 and their product is 1/3.

Let the zero of the polynomial be α and β

According to the question,

α + β = √2

∴ f(x)= x² – (α + β)x + (αβ)

∴ required polynomial f(x)= x² - √2 x + 1/3

Put f(x) = 0

x² - √2 x + 1/3 = 0

3x² – 3√2x + 1 = 0

Find the quadratic polynomial, the sum of whose zeros is 0 and their product is ‒1. Hence, find the zeros of the polynomial.

Find the quadratic polynomial, the sum of whose zeros is and their product is 1. Hence, find the zeros of the polynomial.

If and x = ‒3 are the roots of the quadratic equation ax² + 7x + b = 0 then find the values of a and b.

If (x + a) is a factor of the polynomial 2x² + 2ax + 5x + 10, find the value of a.